Long-time behavior of a coupled heat-wave system using a structure-preserving finite element method
Authors
Ghislain Haine, Denis Matignon, Florian Monteghetti
Abstract
This work is a numerical investigation of the coupling between the heat and wave equations, recast as an interconnection of open port-Hamiltonian systems (pHs). A structure-preserving discretization suited to open pHs, based on a mixed finite element approximation space that includes boundary inputs and outputs, is shown to yield a semi-discrete power balance analogous to the continuous one. In the frequency domain, the semi-discretization captures the finite accumulation point in the spectrum, associated with highly-oscillatory eigenfunctions localized at the interconnection interface. In the time domain, the polynomial and logarithmic energy decays proved by Zhang and Zuazua are recovered using a Crank-Nicolson scheme.
Keywords
polynomial decay, logarithmic decay, Port-Hamiltonian systems, structure-preserving method
Citation
- Journal: Mathematical Reports
- Year: 2022
- Volume: 24
- Issue: 1-2
- Pages: 187–215
- Publisher: Romanian Academy
BibTeX
@article{haine2022longtime,
author={Haine, Ghislain and Matignon, Denis and Monteghetti, Florian},
title={{Long-time behavior of a coupled heat-wave system using a structure-preserving finite element method}},
journal={Mathematical Reports},
volume={24},
number={1--2},
pages={187--215},
year={2022},
publisher={Romanian Academy}
}